Pricing Options on Realized Variance in the Heston Model with Jumps in Returns and Volatility

Journal of Computational Finance, Vol. 11, No. 4, pp. 33-70, 2008

37 Pages Posted: 21 May 2009 Last revised: 5 Oct 2010

Date Written: April 21, 2008

Abstract

We develop analytical methodology for pricing and hedging options on the realized variance under the Heston stochastic variance model (1993) augmented with jumps in asset returns and variance. By employing generalized Fourier transform we obtain analytical solutions (up to numerical inversion of Fourier integral) for swaps on the realized volatility and variance and for options on these swaps. We also extend our framework for pricing forward-start options on the realized variance and volatility, including options on the VIX.

Our methodology allows us to consistently unify pricing and risk managing of different volatility options. We provide an example of model parameters estimation using both time series of the VIX and the VIX options data and find that the proposed model is in agreement with both historical and implied market data. Finally, we derive a log-normal approximation to the density of the realized variance in the Heston model and obtain accurate approximate solution for volatility options with longer maturities.

Keywords: realized variance, variance swap, volatility swap, option on variance swap, volatility derivatives, VIX futures, VIX option, Heston model

JEL Classification: C00

Suggested Citation

Sepp, Artur, Pricing Options on Realized Variance in the Heston Model with Jumps in Returns and Volatility (April 21, 2008). Journal of Computational Finance, Vol. 11, No. 4, pp. 33-70, 2008. Available at SSRN: https://ssrn.com/abstract=1408005

Artur Sepp (Contact Author)

Quantica Capital AG ( email )

Zurich
Switzerland

HOME PAGE: http://artursepp.com

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